Novel topological black holes from thermodynamics and deforming horizons

TL;DR

This paper constructs two new topological black hole solutions with unusual horizon shapes in a holographic axions model, analyzes their thermodynamics using a unified approach, and suggests potential for higher-dimensional generalizations.

Contribution

The paper introduces novel exact topological black hole solutions with deforming horizons and develops an improved thermodynamics method based on the unified first law.

Findings

Constructed two novel black hole solutions with unusual horizon shapes.

Re-derived the thermodynamics framework using the quasi-local approach.

Demonstrated the method's potential for higher-dimensional generalizations.

Abstract

Two novel topological black hole exact solutions with unusual shapes of horizons in the simplest holographic axions model, the four-dimensional Einstein-Maxwell-axions theory, are constructed. We draw embedding diagrams in various situations to display unusual shapes of novel black holes. To understand their thermodynamics from the quasi-local aspect, we re-derive the unified first law and the Misner-Sharp mass from the Einstein equations for the spacetime as a warped product $\M2 \times \Mco2$. The Ricci scalar $\Rhat$ of the sub-manifold $\Mco2$ can be a non-constant. We further improve the thermodynamics method based on the unified first law. Such a method simplifies constructing solutions and hints at generalization to higher dimensions. Moreover, we apply the unified first law to discuss black hole thermodynamics.